The invention relates to a compression ignition direct injection internal combustion engine with an inlet port for inducing rotation of the incoming air about the axis of the cylinder and a combustion chamber or cavity having the shape of a body of rotation and disposed in the piston and accepting, at the end of the compression stroke, almost all the combustion air. This chamber comprises, below the crown of the piston, a constriction that divides it into an upper and a lower portion, and an injection nozzle with its tip arranged substantially on the axis of the combustion chamber. The jets of fuel from the nozzle are directed against the wall of the chamber, and the geometrical point of intersection of the axes of the injection nozzle holes lying below the minimum cross section of the constriction of the combustion chamber or cavity throughout the injection period.